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[Anders Logg <question141904@xxxxxxxxxxxxxxxxxxxxx>]

Question #141904 on DOLFIN changed:
https://answers.launchpad.net/dolfin/+question/141904

    Status: Open => Answered

Anders Logg proposed the following answer:
On Tue, Jan 18, 2011 at 12:47:22PM -0000, Raphael Kruse wrote:
> New question #141904 on DOLFIN:
> https://answers.launchpad.net/dolfin/+question/141904
>
> Hi,
>
> I am looking for a way to implement an integral operator in Python/Dolfin of the following form:
>
> Carleman operator Q : L^2 -> L^2
> Given: an integral kernel q(x,y), where q is symmetric q(x,y) = q(y,x)
>
> For u in L^2 the integral operator Q is given by
> [Qu](x) = \int q(x,y) u(y) dy
>
> In particular, I am interested in determing the eigenvalues and eigenfunctions of Q, i.e.
>
> Qu = \lambda u
>
> Thus, for a finite element approximation I need the matrix
>
> \int \int q(x,y) u(x) v(y) dy dx
>
> where u and v are the trial and test function, respectively.
>
> I am new to Dolfin and sorry if there already is an answer to this question.
>
> Thank you for any help!

I don't think this is possible. As I understand you want 1-dimensional
trial and test functions and integrate that over a 2-dimensional
domain. DOLFIN assumes that everything you integrate has the same
dimension as the domain.

One inefficient way to do this would be to use 2-dimensional trial and
test functions and then sum appropriately over the columns and rows of
the matrix to reduce to 1-dimensional. I haven't thought it through in
detail but it should be possible.

--
Anders

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